If t1 and t2 are the lengths of tangents drawn from two conjugate points A, B then
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see the images you can understant easily
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AB² = t1² + t2²
Step-by-step explanation:
Given t1 and t2 are the lengths of tangents drawn from two conjugate points A , B.
Let 'r' be the radius and 'c' be the centre of the circle.
Since A and B are conjugate points of the circle,
so we have:
AB² = CA² + CB² - 2r² .....................(1)
Now, CA² = t1² + r² ..................(2)
and CB² = t2² + r² ................(3)
From (1), (2) and (3), we get:
AB² = (t1² + r²) + (t2² + r²) - 2r²
AB² = t1² + t2²
Therefore, AB² = t1² + t2² .
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